Defining valid breeding goals for animal breeds

Abstract

Background: The objective of any valid breeding program is to increase the suitability of a breed for its future purposes. The approach most often followed in animal breeding for optimizing breeding goals assumes that the sole desire of the owners is profit maximization. As this assumption is often violated, a generalized approach is needed that does not rely on this assumption.

Results: The generalized approach is based on the niche concept. The niche of a breed is a set of environments in which a small population of the breed would have a positive population growth rate. Its growth rate depends on demand from prospective consumers and supply from producers. The approach involves defining the niche that is envisaged for the breed and identifying the trait optima that maximize the breed's adaptation to its envisaged niche within the set of permissible breeding goals. The set of permissible breeding goals is the set of all potential breeding goals that are compatible with animal welfare and could be reached within the planning horizon of the breeding program. In general, the breed's adaptation depends on the satisfaction of the producers with the animals and on the satisfaction of the consumers with the products produced by the animals. When consumers buy live animals, then the breed needs to adapt to both the environments provided by the producers, and the environments provided by the consumers. The profit function is replaced by a more general adaptedness function that measures the breed's adaptation to its envisaged niche.

Conclusions: The proposed approach coincides with the traditional approach if the producers have the sole desire to maximize their income, and if consumer preferences are well reflected by the product prices. If these assumptions are not met, then the traditional approach to breeding goal optimization is unlikely to result in a valid breeding goal. Using the example of companion breeds, this paper shows that the proposed approach has the potential to fill the gap.

Fig. 1

Illustration of the space $\mathcal{E}$ of environments. Each environment $\mathbf{e}=\left(\mathbf{d},,,\mathbf{v}\right)$ contains a subvector $\mathbf{d}\in \mathcal{D}$ that quantifies the extents to which the owner wants his animal to satisfy certain potential desires. The suitability of a breed to satisfy a certain desire depends on the subvector $\mathbf{v}\in \mathcal{V}$ of influencing variables. Each desire that an owner could associate with owning an animal can have implications for the optimum phenotype and the phenotypic diversity of the species. Thus, it can lead to adaptive or non-adaptive radiation. The figure illustrates what the influencing factors are

Fig. 2

Illustration of the adaptation of a breed to different environments. Illustrative example with a one-dimensional space $\mathcal{E}$ of environments, and a one-dimensional space $\mathcal{Y}$ of phenotypes. The trait of interest is body weight. A small body weight is preferred in environment $e_1$, while a large body weight is preferred in environment $e_2$, so breed $b_1$ is adapted to environment $e_1$, while breed $b_2$ is adapted to environment $e_2$. Note that not only the preferred body weight changes depending on the environment, but also the realized body weight. The animals get heavier in environment $e_2$, e.g., due to improved feed quality

Fig. 3

Illustration of the state space of breeding programs. Illustrative example with a one-dimensional space $\mathcal{E}$ of environments, and a one-dimensional space $\mathcal{Y}$ of phenotypes, so there is only one trait under selection. The current state of the breeding program for breed $b$ is described by a function ${\mu }_b^c\in \mathcal{P}$ that provides for each environment $e$ the trait mean of the breed in that environment. The phenotypic variance is assumed to be constant. The breeding goal of the breed is defined by function ${\dot{\mu }}_b\in \mathcal{P}$. The red arrows symbolize that the trait mean ${\mu }_b^c\left(e\right)$ is expected to approach the breeding goal ${\dot{\mu }}_b\left(e\right)$ in the course of the breeding program for all relevant environments $e$

Fig. 4

Illustration of the proposed method for breeding goal optimisation

Fig. 5

Illustration of the set of permissible breeding goals. Illustrative example with a two-dimensional space of phenotypes. The level sets of the objective function indicate the position of the optimum breeding goal ${\dot{\mathbf{\mu }}}_b^s$ in the search area ${\mathcal{S}}_b$ for the breed. The search area includes the response area of the breed but excludes putative breeding goals that violate ethical constraints. The set ${\mathcal{U}}_b$ of permissible breeding goals is included in the response area. The optimum permissible breeding goal ${\dot{\mathbf{\mu }}}_b^i$ has the property that the level sets of the objective function are tangential to the boundary of ${\mathcal{U}}_b$. The vector from the current trait means ${\mathbf{\mu }}_b^c$ to the optimum permissible breeding goal ${\dot{\mathbf{\mu }}}_b^i$ defines the optimum selection index